scholarly journals Weak limits for the largest subpopulations in Yule processes with high mutation probabilities

2017 ◽  
Vol 49 (3) ◽  
pp. 877-902 ◽  
Author(s):  
Erich Baur ◽  
Jean Bertoin
Keyword(s):  
Total Population ◽  
General Strategy ◽  
Limit Laws ◽  
Percolation Parameter ◽  
Yule Process ◽  
Large Numbers ◽  
Weak Limits ◽  
Poisson Limit ◽  
Neutral Mutations ◽  
Recursive Trees

Abstract We consider a Yule process until the total population reaches size n ≫ 1, and assume that neutral mutations occur with high probability 1 - p (in the sense that each child is a new mutant with probability 1 - p, independently of the other children), where p = pn ≪ 1. We establish a general strategy for obtaining Poisson limit laws and a weak law of large numbers for the number of subpopulations exceeding a given size and apply this to some mutation regimes of particular interest. Finally, we give an application to subcritical Bernoulli bond percolation on random recursive trees with percolation parameter pn tending to 0.

The Demographic Transition Theory of War: Why Young Societies Are Conflict Prone and Old Societies Are the Most Peaceful

2019 ◽  
Vol 43 (3) ◽  
pp. 53-95 ◽  
Author(s):  
Deborah Jordan Brooks ◽  
Stephen G. Brooks ◽  
Brian D. Greenhill ◽  
Mark L. Haas
Keyword(s):  
Young People ◽  
Total Population ◽  
Empirical Examination ◽  
Demographic Transitions ◽  
The Road ◽  
Large Numbers ◽  
The World ◽  
Theory Of War ◽  
First Time

The world is experiencing a period of unprecedented demographic change. For the first time in human history, marked disparities in age structures exist across the globe. Around 40 percent of the world's population lives in countries with significant numbers of elderly citizens. In contrast, the majority of the world's people live in developing countries with very large numbers of young people as a proportion of the total population. Yet, demographically, most of the world's states with young populations are aging, and many are doing so quickly. This first-of-its kind systematic theoretical and empirical examination of how these demographic transitions influence the likelihood of interstate conflict shows that countries with a large number of young people as a proportion of the total population are the most prone to international conflict, whereas states with the oldest populations are the most peaceful. Although societal aging is likely to serve as a force for enhanced stability in most, and perhaps all, regions of the world over the long term, the road to a “demographic peace” is likely to be bumpy in many parts of the world in the short to medium term.

Asymptotic final size distribution of the multitype Reed–Frost process

1986 ◽  
Vol 23 (03) ◽  
pp. 563-584
Author(s):  
Gianpaolo Scalia-Tomba
Keyword(s):  
Size Distribution ◽  
Total Population ◽  
Large Population ◽  
Asymptotic Distributions ◽  
Reproduction Rate ◽  
Final Size ◽  
Basic Reproduction Rate ◽  
Infection Pattern ◽  
Large Numbers ◽  
A Chain

The asymptotic final size distribution of a multitype Reed–Frost process, a chain-binomial model for the spread of an infectious disease in a finite, closed multitype population, is derived, as the total population size grows large. When all subgroups are of comparable size, the infection pattern irreducible and the epidemic started by a small number of initial infectives, the classical threshold behaviour is obtained, depending on the basic reproduction rate of the disease in the population, and the asymptotic distributions for small and large outbreaks can be found. The same techniques can then be used to study other asymptotic situations, e.g. small groups in an otherwise large population, large numbers of initial infectives and reducible infection patterns.

Functional limit theorems for stochastic processes based on embedded processes

1975 ◽  
Vol 7 (01) ◽  
pp. 123-139 ◽  
Author(s):  
Richard F. Serfozo
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Limit Theorems ◽  
Functional Limit ◽  
Functional Limit Theorems ◽  
Limit Laws ◽  
Iterated Logarithm ◽  
Large Numbers ◽  
Subordinated Processes ◽  
Analogous Functional

The techniques used by Doeblin and Chung to obtain ordinary limit laws (central limit laws, weak and strong laws of large numbers, and laws of the iterated logarithm) for Markov chains, are extended to obtain analogous functional limit laws for stochastic processes which have embedded processes satisfying these laws. More generally, it is shown how functional limit laws of a stochastic process are related to those of a process embedded in it. The results herein unify and extend many existing limit laws for Markov, semi-Markov, queueing, regenerative, semi-stationary, and subordinated processes.

Central Limit Theorems for Additive Tree Parameters with Small Toll Functions

2014 ◽  
Vol 24 (1) ◽  
pp. 329-353 ◽  
Author(s):  
STEPHAN WAGNER
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Normal Limit ◽  
Central Limit Theorems ◽  
Limit Laws ◽  
Polya Trees ◽  
Additive Tree ◽  
Log Normal ◽  
Recursive Trees ◽  
Parameter Values

We call a tree parameter additive if it can be determined recursively as the sum of the parameter values of all branches, plus a certain toll function. In this paper, we prove central limit theorems for very general toll functions, provided that they are bounded and small on average. Simply generated families of trees are considered as well as Pólya trees, recursive trees and binary search trees, and the results are illustrated by several examples of parameters for which we prove normal or log-normal limit laws.

scholarly journals Problems and Challenges to Determine Pesticide Residues in Nepal

2019 ◽  
Vol 8 (2) ◽  
pp. 97-106
Author(s):  
Bibek Raj Bhattarai ◽  
Babita Aryal ◽  
Bikash Adhikari ◽  
Niranjan Parajuli
Keyword(s):  
Climate Change ◽  
Pesticide Residues ◽  
Total Population ◽  
Public Awareness ◽  
Global Market ◽  
Agriculture Sector ◽  
Large Numbers ◽  
Harmful Organisms ◽  
Increasing Demand ◽  
Agriculture Products

Nepal is predominately an agrarian country where still the majority of the total population rely on agriculture (Adhikari, 2018). The productivity of agriculture should be augmented to fulfill the increasing demand for food. Despite countless efforts, the agriculture sector could not come across to accomplish the global market for foodstuffs due to climate change. By which, plants will be attacked by various insects, funguses, and microorganisms. To tackle such problems, pesticides are being widely used to defend and block agriculture products from harmful organisms. But due to lack of public awareness, large numbers of farmers have been using pesticides as medicine - a conviction implanted in their mind (Pingali et al., 1995).

scholarly journals Adaptation of constant effort sampling and of removal trapping for the estimation of populations of microscopic organisms in dense substrates ()

1980 ◽  
Vol 10 (3) ◽  
pp. 535-544 ◽  
Author(s):  
Ilse Walker ◽  
Maryolanda Trindade Lages
Keyword(s):  
Total Population ◽  
Time Interval ◽  
Terra Firme ◽  
Relative Population ◽  
Depletion Effect ◽  
Large Numbers ◽  
Microscopic Field ◽  
Small Streams ◽  
Terra Firme Forest ◽  
And Performance

Abstract Large numbers of thecamoebae are found in the sand and detritus substrate of small streams in the Amazonian terra firme forest. Their relative population densities can be determined by searching and counting thecae under a dissecting microscope for a standard time interval (constant effort sampling). The total population per sample can be calculated from a gradual linear depletion during successive such counts in a given sample (removal trapping). From a series of such regressions the total number of thecamoebae of any sample can be estimated from a single, first count. The method depends on specific conditions with regard to size of area searched, quantity of substrate per area, density of organisms per substrate and performance of the observers. These conditions are generally valid for similar methodical treatment of any population of small organisms in any type of dense substrate. The linear regression of the depletion effect implies a constant mean probability for any thecamoeba to be found in the specified substrate during the specified time interval by any of the three observers involved in the study, and this despite the uncontrollable subjectivity of visual search in a microscopic field.

scholarly journals A Strong Law for the Size of Yule M-Oriented Recursive Trees

2012 ◽  
Vol 8 (2) ◽  
pp. 67-72
Author(s):  
Mehri Javanian ◽  
Mohammad Q. Vahidi-Asl
Keyword(s):  
Exact Distribution ◽  
Birth Rates ◽  
Strong Law ◽  
Recursive Tree ◽  
Yule Process ◽  
Recursive Trees

Abstract Let Nt be the total number of nodes in a Yule m-oriented recursive tree at time t. Then {Nt : t ∈ [0;1)} is a Yule process with birth rates λn = (m(n - 1) + 1)λ for n ≥ 1, where N0 = 1. In this paper, we first give the exact distribution of Nt, then prove that , almost surely

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